Q32 of 77 Page 7


If the points (2, 1) and (1, -2) are equidistant from the point (x, y), showthat x + 3y = 0.


SOLUTION:

Let the points A(2, 1) and B(1, -2) be at equidistant from the point P(x, y).

⇒

⇒ (x - 2) 2 + (y - 1) 2 = (x - 1) 2 + (y + 2) 2

⇒ x 2 – 4x + 4 + y 2 – 2y + 1 = x 2 – 2x + 1 + y 2 + 4y + 4
⇒ – 4x + 4 – 2y + 1 = - 2x + 1 + 4y + 4

⇒ – 2x – 6y = 0

⇒ x + 3y = 0.

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